# How do you simplify sqrt(6n)(7n^3+sqrt12)?

Aug 30, 2016

First get rid of the parentheses by using the distribution rule:

#### Explanation:

$= \sqrt{6 n} \times 7 {n}^{3} + \sqrt{6 n} \times \sqrt{12}$

You may want to rearrange:
$= 7 {n}^{3} \times \sqrt{6 n} + \sqrt{6 n \times 12}$
$= 7 {n}^{3} \sqrt{6 n} + \sqrt{6 \times 6 \times 2 \times n}$
$= 7 {n}^{3} \sqrt{6 n} + \sqrt{6 \times 6} \times \sqrt{2 \times n}$

Now take out the only square:
$= 7 {n}^{3} \sqrt{6 n} + 6 \sqrt{2 n}$

This is not much of a simplification, but it's as far as this goes.